Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}8x-2y &= 8 \\ -8x+9y &= 6\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-8x = -9y+6$ Divide both sides by $-8$ to isolate $x$ $x = {\dfrac{9}{8}y - \dfrac{3}{4}}$ Substitute this expression for $x$ in the first equation. $8({\dfrac{9}{8}y - \dfrac{3}{4}}) - 2y = 8$ $9y - 6 - 2y = 8$ Simplify by combining terms, then solve for $y$ $7y - 6 = 8$ $7y = 14$ $y = 2$ Substitute $2$ for $y$ in the top equation. $8x-2( 2) = 8$ $8x-4 = 8$ $8x = 12$ $x = \dfrac{3}{2}$ The solution is $\enspace x = \dfrac{3}{2}, \enspace y = 2$.